Correlation control for pure and efficiently generated heralded single photons

We present a detailed study on the properties of single photons generated by spontaneous parametric down conversion (SPDC) when both the spectral and spatial degrees of freedom are controlled by means of filters. Our results show that it is possible to obtain pure heralded single photons with high heralding efficiency despite the use of filters. Moreover, we report an asymmetry on the single-photon properties exhibited in type-II SPDC sources that depends on choosing the signal or the idler photon as the heralding one.

Figure 1

Experimental setup for a HSP source using a type-II BBO crystal in a collinear configuration. A dichroic mirror (DM) is used for stoping the pump, and a polarizing beamsplitter (PBS) separates the down-converted photons according to their polarization. Spatial (SpaF) and spectral (SpeF) filters are placed in the heralding- and heralded-photon paths. In (a), the idler (ordinary-polarized photon) is the HSP, while in (b) the signal (extraordinary-polarized photon) is the HSP.

Figure 2

Illustration of the correlations associated with the SPDC photon pair generation. In (a), the two-photon system is viewed as composed by the spatial and spectral variables of each photon. Along this work, the correlation between these two degrees of freedom is controlled by means of filters. In (b), the two-photon system is considered as one given by the signal variables and the other by the idler ones. The signal-idler correlation is mediated through the pump properties.

Figure 3

Effect of filtering on the spectral joint spectrum for collinear type-II SPDC. In (a) spectral filters are not considered, while in (b) both arms are filtered using the same filter bandwidth. In (c) and (d) only one of the photons is spectrally filtered.

Figure 4

Effect of filtering on the spatial joint spectrum for collinear type-II SPDC. In (a) spatial filters are not considered, while in (b) both arms are filtered using the same collecting mode. In (c) and (d) only one of the photons is spatially filtered.

Figure 5

Pictorial representation of the conditions considered to study the spatial HSP properties. (a) Scheme indicating that spatial filters vary and the spectral filters are fixed. This is symbolized through variable and fixed knobs. (b) Cartoon showing the different correlations when the spatial-spectral correlation exists (upper part), and when such correlation is completely broken (lower part).

Figure 6

Spatial HSP properties when the collecting modes of both photons, signal and idler, are equal and vary simultaneously. The pump properties are ${\sigma }_p=1.0$ nm and ${\mathit{w}}_p=10\mu \mathrm{m}$. In (a), we plot purities and heralding efficiencies for the case in which the spatial-spectral correlation is present (${\sigma }_s={\sigma }_i=5.0$ nm). In (b), HSP properties when the spatial-spectral correlation is broken (${\sigma }_s={\sigma }_i=0.1$ nm).

Figure 7

HSP properties as a function of the signal and idler collecting modes when they vary independently. We show contour plots for the spatial HSP purity (a) and heralding efficiencies, ${\eta }_s$ and ${\eta }_i$, in (b) and (c), respectively.

Figure 8

Pictorial representation of the conditions considered to study the spectral HSP properties. (a) Scheme indicating that spatial filters are fixed and the spectral filters vary. (b) Cartoon showing the different correlations when the spatial-spectral correlation exists (upper part), and when such correlation is completely broken (lower part).

Figure 9

Spectral HSP properties when the spectral-filter bandwidths of both photons, signal and idler, are equal and vary simultaneously. The pump properties are ${\sigma }_p=1.0$ nm and ${\mathit{w}}_p=10\mu \mathrm{m}$. In (a), we plot purities and heralding efficiencies for the case in which the spatial-spectral correlation is present (${\mathit{w}}_s={\mathit{w}}_i=50$ $\mu \mathrm{m}$). In (b), HSP properties when the spatial-spectral correlation is broken (${\mathit{w}}_s={\mathit{w}}_i=100$ $\mu \mathrm{m}$).

Figure 10

Pictorial representation of the conditions considered to study the behavior of PEFs. (a) Scheme indicating that spatial filters are fixed and only one of the spectral filters varies. (b) Cartoon showing two different strengths for the spectral signal-idler correlation. The multiple lines in the lower part indicates that the spectral correlation is stronger than in the upper part.

Figure 11

PEF for a specific value of the spectral correlation between signal and idler. The pump properties are ${\sigma }_p=1.0$ nm and ${\mathit{w}}_p=10\mu \mathrm{m}$, and the spatial-spectral correlation is present making ${\mathit{w}}_s={\mathit{w}}_i=50$ $\mu \mathrm{m}$. In (a), we plot idler's PEF when this photon is the HSP, while in (b) the PEF is shown when the signal is the HSP.

Figure 12

PEF when the spectral signal-idler spectral correlation is stronger than in Fig. 11. The pump properties are ${\sigma }_p=0.1$ nm and ${\mathit{w}}_p=10\mu \mathrm{m}$, and the spatial-spectral correlation is present making ${\mathit{w}}_s={\mathit{w}}_i=50$ $\mu \mathrm{m}$. In (a), we plot idler's PEF when this photon is the HSP, while in (b) the PEF is shown when the signal is the HSP.